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Simplifying x2 + -4x + -11 = 30 Reorder the terms: -11 + -4x + x2 = 30 Solving -11 + -4x + x2 = 30 Solving for variable 'x'. Reorder the terms: -11 + -30 + -4x + x2 = 30 + -30 Combine like terms: -11 + -30 = -41 -41 + -4x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -41 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -4x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + -4x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -4x + x2 = 0 + 41 -4x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 -4x + x2 = 41 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 41 + 4 Reorder the terms: 4 + -4x + x2 = 41 + 4 Combine like terms: 41 + 4 = 45 4 + -4x + x2 = 45 Factor a perfect square on the left side: (x + -2)(x + -2) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -2) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -2 = 6.708203933 Simplifying x + -2 = 6.708203933 Reorder the terms: -2 + x = 6.708203933 Solving -2 + x = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.708203933 + 2 x = 6.708203933 + 2 Combine like terms: 6.708203933 + 2 = 8.708203933 x = 8.708203933 Simplifying x = 8.708203933Subproblem 2
x + -2 = -6.708203933 Simplifying x + -2 = -6.708203933 Reorder the terms: -2 + x = -6.708203933 Solving -2 + x = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.708203933 + 2 x = -6.708203933 + 2 Combine like terms: -6.708203933 + 2 = -4.708203933 x = -4.708203933 Simplifying x = -4.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.708203933, -4.708203933}
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